Package 'SMNlmec'

Bayesian Censored Mixed-Effects Models with Damped Exponential Correlation Structures for Scale Mixture of Normal distributions error

Description

This function fits left, right censored mixed-effects linear model, with scale mixture of normal distribution errors, using the Stan. It returns estimates, standard errors and LPML, AIC, BIC and DIC.

Usage

SMNlmec.est(
  ID,
  x_set,
  z_set,
  tt,
  y_complete,
  censor_vector,
  dist = "Normal",
  struc = "UNC",
  direction = "left",
  thin_num = 1,
  chains_num = 1,
  iter_num = 3000,
  burn_percen = 0.1,
  seed_set = NULL,
  adapt_delta_set = 0.8
)

Arguments

ID	Vector N x 1 of the ID of the data set, specifying the ID for each measurement.
x_set	Design matrix of the fixed effects of order N x p.
z_set	Design matrix of the random effects of order N x d.
tt	Vector N x 1 with the time the measurements were made, where N is the total number of measurements for all individuals. Default it's considered regular times.
y_complete	Vector N x 1 of the complete responses.
censor_vector	Vector N x 1 of the indicator vector of censored responses.
dist	Distribution of the random effects and random error. Available options are Normal, Student and Slash.
struc	Structure of the correlation structure. Available options are UNC, DEC, CAR.
direction	Direction of censoring type. Available options are left and right.
thin_num	A positive integer specifying the period for saving samples. The default is 5. See more details in rstan::stan().
chains_num	A positive integer specifying the number of chains generating by rstan::stan(). The default is 3.
iter_num	A positive integer specifying the number of iterations for each chain (including warmup). The default is 5000.
burn_percen	A percentage of the warm-up iterations in each chain the Stan. The default is 0.2.
seed_set	A random seed. The default is NULL.
adapt_delta_set	A parameter to control the sampler's behavior. The default is 0.8. See rstan::stan() for more details.

Value

Return a S4 class SMNlmecfit object. Using function SMNlmec.summary() to obtain the estimation of parameters and model selection criteria. The SMNlmecfit include:

stan_object	A stanfit object from rstan::stan().
model_criteria	A list includes LPML, DIC, EAIC, EBIC, K-L divergence.
dist_set	The setting of distribution of the stan model.
struc_set	The setting of correlation structure of the stan model.

References

Kelin Zhong, Fernanda L. Schumacher, Luis M. Castro and Victor H. Lachos. Bayesian analysis of censored linear mixed-effects models for heavy-tailed irregularly observed repeated measures. Statistics in Medicine, 2025. doi:10.1002/sim.10295

Examples

require(rstan)
require(StanHeaders)
require(MASS)
require(tmvtnorm)
require(mvtnorm)
require(mnormt)

data("UTIdata_sub")
data1 <- UTIdata_sub
y1 <- c(log10(data1$RNA))
cc <- (data1$RNAcens==1)+0
y_com<-as.numeric(y1)
rho_com<-as.numeric(cc)
x <- cbind(
 (data1$Fup==0)+0,
 (data1$Fup==1)+0,
 (data1$Fup==3)+0,
 (data1$Fup==6)+0,
 (data1$Fup==9)+0,
 (data1$Fup==12)+0,
 (data1$Fup==18)+0,
 (data1$Fup==24)+0
 )
z <- matrix(rep(1, length(y1)), ncol=1)

UTI_T_DEC <- SMNlmec.est(ID = data1$Patid, x_set = x, z_set = z,
                         tt = data1$Fup, y_complete = y_com,
                         censor_vector = rho_com, dist = "Student",
                         struc = "DEC", direction = "left",
                         thin_num = 1, chains_num = 1, iter_num = 3000,
                         burn_percen = 0.1, seed_set = 9955,
                         adapt_delta_set = 0.8)

SMNlmec.summary(UTI_T_DEC)

---

Generating Censored UNC, DEC, CAR errors with Mixed Effects, for normal, student's-t and slash distribution.

Description

Generating Censored UNC, DEC, CAR errors with Mixed Effects, for normal, student's-t and slash distribution.

Usage

SMNlmec.sim(
  m,
  x,
  z,
  tt,
  nj,
  beta,
  sigma2,
  D,
  phi,
  struc = "UNC",
  typeModel = "Normal",
  p.cens = 0.1,
  n.cens = NULL,
  cens_type = "right",
  nu_set = NULL
)

Arguments

m	Number of individuals.
x	Design matrix of the fixed effects of order N x p, corresponding to vector of fixed effects.
z	Design matrix of the random effects of orderN x d, corresponding to vector of random effects.
tt	Vector N x 1 with the time the measurements were made, where N is the total number of measurements for all individuals.
nj	Vector m x 1 with the number of measurements of each individual, where m is the total number of individuals.
beta	Vector of values fixed effects.
sigma2	Values of the scalar of the variance matrix.
D	Variance matrix of the random effects of order d x d.
phi	Vector of parameter in the DEC and CAR structure. NULL for UNC, c(phi_1,phi_2) for DEC and c(phi_1,1) for CAR.
struc	Structure for the simulated data. Available options are UNC, DEC and CAR.
typeModel	Distribution of the simulated data. Available options are Normal, Student and Slash.
p.cens	Percentage of censored measurements in the responses. The default value is 0.1.
n.cens	Number of censored measurements in the responses. The default value is NULL.
cens_type	The direction of cesoring. Available options are left and right.
nu_set	degrees of freedom for student's-t or slash simulated data. The default value is NULL.

Value

return list:

cc	Vector of censoring indicators.
y_cc	Vector of responses censoring.

Examples

p.cens <- 0.1
m <- 50
D <- matrix(c(0.049,0.001,0.001,0.002),2,2)
sigma2_set <- 0.15
beta <- c(-2.83,-0.18)
nu <- 2
phi <- c(0.6,2)
nj <- rep(6,m)
tt <- rep(1:6,length(nj))
X1 <- rep(1,sum(nj))
X2 <- tt
x <- as.matrix(cbind(X1,X2))
Z1 <- rep(1,sum(nj))
Z2 <- tt
z <- as.matrix(cbind(Z1,Z2))

ID_sim <- rep(0,length(tt))
ID_log <- 0
for(i in 1:m) {
  for(j in 1:nj[i]) {
    ID_sim[ID_log + j] <- i
  }
  ID_log <- ID_log + nj[i]
}

Slash_DEC_sim <- SMNlmec.sim(m = m,x = x,z = z,tt = tt,nj = nj,beta = beta,
                      sigma2 = sigma2_set,D = D,phi= phi,struc ="DEC",
                      typeModel="Slash",p.cens = p.cens,n.cens = NULL,
                      cens_type="right",nu_set=nu)

head(Slash_DEC_sim$cc)
sum(Slash_DEC_sim$cc)/length(Slash_DEC_sim$cc)

head(Slash_DEC_sim$y_cc)


y_com <- as.numeric(Slash_DEC_sim$y_cc)
rho_com <- as.numeric(Slash_DEC_sim$cc)
tem <- tt

Slash_DEC_est <- SMNlmec.est(ID = ID_sim, x_set = x, z_set = z,
                         tt = tem, y_complete = y_com,
                         censor_vector = rho_com, dist = "Slash",
                         struc = "DEC", direction = "right",
                         thin_num = 1, chains_num = 1, iter_num = 3000,
                         burn_percen = 0.1, seed_set = 9955,
                         adapt_delta_set = 0.8)

SMNlmec.summary(Slash_DEC_est)

---

SMNlmecfit Summary

Description

A generic function to provide a summary for objects of class SMNlmecfit.

Usage

SMNlmec.summary(object)

## S4 method for signature 'SMNlmecfit'
SMNlmec.summary(object)

Arguments

object

An object of class SMNlmecfit.

Value

A summary of model estimations, R-hats, standard errors, and criteria.

A printed summary of the SMNlmecfit object.

---

SMNlmecfit Class

Description

SMNlmecfit Class

Slots

stan_object

stanfit object from rstan.

model_criteria

list, model selection criteria.

dist_set

character, the name of distribution.

struc_set

character, the name of correlation structure.

---

Create SMNlmecfit Objects

Description

A function to create objects of class SMNlmecfit.

Usage

SMNlmecfit.creator(stan_object, model_criteria, dist_set, struc_set)

Arguments

stan_object	stanfit object from rstan.
model_criteria	list, model selection criteria.
dist_set	character, the name of distribution.
struc_set	character, the name of correlation structure.

Value

A SMNlmecfit object containing:

stan_object	A stanfit object from rstan::stan().
model_criteria	A list includes LPML, DIC, EAIC, EBIC, K-L divergence.
dist_set	The setting of distribution of the stan model.
struc_set	The setting of correlation structure of the stan model.

---

Data set for Unstructured Treatment Interruption Study

Description

Data set from a study of Unstructured Treatment Interruption in HIV-infected adolescents in four institutions in the US. The main outcome is the HIV-1 RNA viral load, which is subject to censoring below the lower limit of detection of the assay (50 copies/mL). The censored observations are indicated by the variable RNAcens.

Usage

data(UTIdata)

Format

A data frame with 373 observations on the following 5 variables.

Patid

patient ID

Days.after.TI

days after treatment interruption.

Fup

follow-up months

RNA

viral load RNA

RNAcens

censoring indicator for viral load

References

Saitoh, A., Foca, M, et al. (2008), Clinical outcome in perinatally acquired HIV-infected children and adolescents after unstructured treatment interruption, Pediatrics,121, e513-e521.

---

Sub data set for Unstructured Treatment Interruption Study

Description

Data set from a study of Unstructured Treatment Interruption in HIV-infected adolescents in four institutions in the US. The main outcome is the HIV-1 RNA viral load, which is subject to censoring below the lower limit of detection of the assay (50 copies/mL). The censored observations are indicated by the variable RNAcens. Excluding subjects whose observations are less than 2 and with missing RNA (excluding subject ID C6 T16).

Usage

data(UTIdata_sub)

Format

A data frame with 360 observations on the following 5 variables.

Patid

patient ID

Days.after.TI

days after treatment interruption.

Fup

follow-up months

RNA

viral load RNA

RNAcens

censoring indicator for viral load

References

Saitoh, A., Foca, M, et al. (2008), Clinical outcome in perinatally acquired HIV-infected children and adolescents after unstructured treatment interruption, Pediatrics,121, e513-e521.

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